How to inset (or fill in) a complicated mesh?
There are a few ways that you could potentially approach this:


Manually select 4 vertices, press f to make a face, and repeat until you go crazy.
Select all of the vertices and press f to make an "n-gon", you'll quickly realize why n-gons are avoided.
Another option is the Face Tools built into Blender.

From the Manual:


  Fill
  
  The Fill option will create triangular faces from any group of selected edges or vertices, as long as they form one or more
  complete perimeters.
  
  Note, unlike creating n-gons, fill supports holes.
  
  Beauty Fill
  
  
  Mode: Edit Mode
  Menu: Mesh ‣ Faces ‣ Fill/Beautify Fill
  Hotkey: Alt-Shift-F
  
  
  Beautify Fill works only on selected existing faces. It [rearranges] selected triangles to obtain more “balanced” ones (i.e.
  less long thin triangles).


Check out the Manual link. It's got even more information.